Find the x and y Intercepts f(x)=(x^2+9x+18)/(3x+4)

Consider the form ${\displaystyle x^2+bx+c}$. Find a pair of integers whose product is ${\displaystyle c}$ and whose sum is ${\displaystyle b}$. In this case, whose product is ${\displaystyle 18}$ and whose sum is ${\displaystyle 9}$.

Write the factored form using these integers.

Set ${\displaystyle x+3}$ equal to ${\displaystyle 0}$.

Subtract ${\displaystyle 3}$ from both sides of the equation.

Set ${\displaystyle x+6}$ equal to ${\displaystyle 0}$.

Subtract ${\displaystyle 6}$ from both sides of the equation.

Raising ${\displaystyle 0}$ to any positive power yields ${\displaystyle 0}$.

Multiply ${\displaystyle 9}$ by ${\displaystyle 0}$.

Add ${\displaystyle 0}$ and ${\displaystyle 0}$.

Add ${\displaystyle 0}$ and ${\displaystyle 18}$.

Multiply ${\displaystyle 3}$ by ${\displaystyle 0}$.

Add ${\displaystyle 0}$ and ${\displaystyle 4}$.

Factor ${\displaystyle 2}$ out of ${\displaystyle 18}$.

Cancel the common factors.